The solution of the differential equation d y/y + dx/x = 0 is
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The answer is given below :
RULE :
∫dx/x = logx + c, c = integral constant
SOLUTION :
Given,
dy/y + dx/x = 0
On integration, we get
∫dy/y + ∫dx/x = logc, logc = integral constant
⇒ logy + logx = logc
⇒ log(yx) = logc, since log(ab) = loga + logb
⇒ yx = c
⇒ xy = c,
which is the required solution.
Thank you for your question.
RULE :
∫dx/x = logx + c, c = integral constant
SOLUTION :
Given,
dy/y + dx/x = 0
On integration, we get
∫dy/y + ∫dx/x = logc, logc = integral constant
⇒ logy + logx = logc
⇒ log(yx) = logc, since log(ab) = loga + logb
⇒ yx = c
⇒ xy = c,
which is the required solution.
Thank you for your question.
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